Color this Polynomial
Simplified
A visualization method for simplifying expressions.
A GEMS Submission/ALEX
Submitted by: E. Thompson, PhD.
Summer 2008
Why this method works:
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Helps organize like terms
Eliminates overlooking a term
Keeps everything from ‘running together’
Can be used on a problem with any level of
difficulty
• Can be re-visited with solving equations
Use color to change the way you
visualize the problem:
2x – 3y +2x 2 – 6x +9y - Original Problem
2x – 3y +2x 2 – 6x +9y - Find all x’s
2x – 3y +2x 2 – 6x +9y - Find all y’s
2x – 3y +2x 2 – 6x +9y - Find all x 2
-4x +6y +2x 2 - Combine like terms
+2x 2 -4x +6y – Highest power in front
Final Answer: 2x 2 -4x +6y
The simple process
Go through the problem and highlight things that are alike.
Variation with shapes:
(Colors not required)
2x – 3y +2x 2 – 6x +9y - Original Problem
2x – 3y +2x 2 – 6x +9y - Find all x’s
2x – 3y +2x 2 – 6x +9y - Find all y’s
2x – 3y +2x 2 – 6x +9y - Find all x 2
-4x +6y +2x 2 - Combine like terms
+2x 2 -4x +6y – Highest power in front
Final Answer: 2x 2 -4x +6y
Increased Difficulty
2(x – y)+ 2y-3x +x2y Original Problem
2(x – y)+ 2y -3x +x2y
2x –2y + 2y -3x +x2y
-x + 0y +x2y
-x +x2y
x2y -x
Remove Parenthesis
Group with color
Simplify
Regroup
Final Answer
Continue with class samples and individual practice.